Multi-Objective Optimization Design of Low-Frequency Band Gap for Local Resonance Acoustic Metamaterials Based on Genetic Algorithm

Driven by the urgent demand for low-frequency vibration and noise control in engineering scenarios such as automobiles, acoustic metamaterials (AMs), as a new class of functional materials, have demonstrated significant application potential. This paper proposes a low-frequency band gap optimization design method for local resonance acoustic metamaterials (LRAMs) based on a multi-objective genetic algorithm. Within a COMSOL Multiphysics 6.2 with MATLAB R2024b co-simulation framework, a parameterized unit cell model of the metamaterial is constructed. The optimization process targets two objectives: minimizing the band gap’s deviation from the target and reducing the structural mass. A multi-objective fitness function is formulated by incorporating the band gap deviation and structural mass constraints, and non-dominated sorting genetic algorithm II (NSGA-II) is employed to perform a global search over the geometric parameters of the resonant unit. The resulting Pareto-optimal solution set achieves a unit cell mass as low as 26.49 g under the constraint that the band gap deviation does not exceed 2 Hz. The results of experimental validation show that the optimized metamaterial configuration reduces the peak of the low-frequency frequency response function (FRF) at 63 Hz by up to 75% in a car door structure. Furthermore, the simulation predictions exhibit good agreement with the experimental measurements, confirming the effectiveness and reliability of the proposed method in engineering applications. The proposed multi-objective optimization framework is highly general and extensible and capable of effectively balancing between the acoustic performance and structural mass, thus providing an efficient engineering solution for low-frequency noise control problems.